The government sets out plans to rival the Tories' Swedish model for England's schools today with proposals to expand its academy scheme to allow ­universities and businesses to run some of the ­country's worst-performing primaries.

The prime minister and his education secretary, Ed Balls, will enable failing primaries and secondaries to join "chains" of schools controlled by universities, companies, top state schools and colleges.

The tycoon owner of a carpet company is among those given approval to take control of the schools.

Lord Harris, who founded Carpetright and already runs several London academies, is included in a list of sponsors who will be allowed to run multiple schools.

Chester and Sunderland universities and Bradford and Hull colleges have also each been allowed to run two schools.

Local authorities will be expected to call in the sponsors to improve under-performing schools in their area, the Department for Children, Schools and Families said.

The move comes after the Conservative party announced plans, based on a Swedish model, to allow parents, charities and trusts to run their own schools. The government said its plan had been developed "to respond to calls from parents to give them a greater voice".

The DCSF said that within five years, it hoped there would be enough sponsors to reach failing schools across the country.

The prime minister said sponsors should be allowed to run primary schools, rather than just academies, because "it is at primary school where we learn the basic skills on which we will depend".

He said: "If a primary school is not continually striving to improve; if it's not dedicated completely and utterly to developing the full potential of every child that comes through it's gates – it is holding back our children at one of the most critical stages of learning in their lives."

"Local authorities will be able to draw on the world-class excellence in these new chains to drive up standards in weaker schools. And primary schools themselves will be able to opt to join a chain. The evidence is clear – schools often work best when they work together. When schools partner with other schools - operating under a common leadership brand, with a shared ethos, and a shared commitment to excellence – standards are raised for all; the stronger schools and the weaker schools."

The prime minister is expected to flesh out the plans today at Woodberry Down School in Hackney, east London.

Balls said the organisations that had been chosen had track records in running several schools that needed extra support.

He said: "This announcement is about putting the best school leaders at the heart of making our schools system great. The successful schools and organisations announced today are amongst the most outstanding school providers in the country. We want to see every part of the country covered by the programme."

John Bangs, the head of education at the National Union of Teachers criticised the plans. "This is a bizarre idea. Sponsors squeeze out the voice of parents and local authorities and brand schools," he said.